In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
7. Non-Right Triangles
Law of Sines
Problem 1
Textbook Question
In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.
Verified step by step guidance1
Identify the given information: angle A = 34°, angle B = 68°, and side a = 4.8 opposite angle A.
Calculate the third angle C using the triangle angle sum property: \(C = 180^\circ - A - B\).
Use the Law of Sines to relate sides and angles: \(\frac{a}{\sin A} = \frac{b}{\sin B}\).
Rearrange the Law of Sines formula to solve for side b: \(b = \frac{a \cdot \sin B}{\sin A}\).
Substitute the known values of a, A, and B into the formula and prepare to calculate b (do not compute the final value).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Sum Property of a Triangle
The sum of the interior angles in any triangle is always 180°. Knowing two angles allows you to find the third by subtracting their sum from 180°, which is essential for solving oblique triangles.
Recommended video:
Sum and Difference of Tangent
Law of Sines
The Law of Sines relates the sides and angles of a triangle: (a/sin A) = (b/sin B) = (c/sin C). It is used to find unknown sides or angles in oblique triangles when given some combination of sides and angles.
Recommended video:
Intro to Law of Sines
Rounding and Approximation
When solving trigonometric problems, especially with decimals, rounding to a specified precision (here, the nearest tenth) is important for clarity and practical use. This involves using appropriate significant figures after calculation.
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How to Use a Calculator for Trig Functions
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